New types of battery submodules have been developed which include stacked (e.g., interleaved) layers of battery cells, insulation (e.g., thermal and/or electrical), and fins (e.g., for drawing out heat from the interior of the battery submodule). The cells in such battery submodules perform better when they are under slight pressure and therefore the assembly process produces a battery submodule where the can compresses its contents. New assembly devices which can more quickly and/or reliably assemble such battery submodules would be desirable.